Model of pattern formation in epithelial morphogenesis.

One of the most universal events in morphogenesis is the formation of domains of morphologically polarized cells in the initially homogeneous epithelial sheets. We investigate the possibility of considering this process as a phenomenon of self-organization which is based upon the following experimentally proven mechanochemical cell properties: (1) a capacity of individual cells for morphological polarization considered as a bistable "all-or-none" transition of a cell from a non-polarized to a polarized state; (2) transmission of this capacity from one cell to another on their contacts; (3) feedback relations between co-operative cell polarization and tangential elastic tensions in a cell sheet: cell polarization increases tangential tensions whereas the latter inhibit further cell polarization. We have constructed a phenomenological model which formally expresses the above properties. Its mathematical description includes but few macroscopic parameters available to experimental investigation and controlled changes. The analysis of the collective dynamic regimes of cell polarization demonstrates that variations of some non-specific parameters leads to spontaneous transition in the morphology of cell layers accompanied by symmetry breaking (Turing's instability). Under these conditions either long-range ordered patterns of cell polarization (including hexagonal cell nets) or non-regular spotted structures can emerge. In the particular case of a sheet having fixed complete dimensions and lacking any external elastic bonds a stable macrostate is created; it corresponds to the sheet's binary subdivision into polarized and non-polarized cell domains of size-invariant proportions. The model conclusions are compared with the morphogenetical processes in sea-urchin development, the morphogenesis of skin derivates and artificially induced budding in hydrozoa.